# Copositive matrix

Copositive matrix

In mathematics, specifically linear algebra, a real matrix A is copositive if

$x^TAx\geq 0$

for every nonnegative vector $x\geq 0$. The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real positive-definite matrices.

Copositive matrices find applications in economics, operations research, and statistics.

## References

• Berman, Abraham; Robert J. Plemmons (1979). Nonnegative Matrices in the Mathematical Sciences. Academic Press. ISBN 0-12-092250-9.
• Copositive matrix at PlanetMath

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• List of matrices — This page lists some important classes of matrices used in mathematics, science and engineering: Matrices in mathematics*(0,1) matrix a matrix with all elements either 0 or 1. Also called a binary matrix . *Adjugate matrix * Alternant matrix a… …   Wikipedia

• Список матриц — Структура матрицы Здесь собраны наиболее важные классы матриц, используемые в математике, науке (в целом) и прикладной науке (в частности). Под матрицей понимается прямоугольный массив чисел …   Википедия

• List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

• Choi's theorem on completely positive maps — In mathematics, Choi s theorem on completely positive maps (after Man Duen Choi) is a result that classifies completely positive maps between finite dimensional (matrix) C* algebras. An infinite dimensional algebraic generalization of Choi s… …   Wikipedia

• Peres-Horodecki criterion — The Peres Horodecki criterion is a necessary condition, for the joint density matrix ho of two systems A and B, to be separable. It is also called the PPT criterion, for positive partial transpose . In the 2x2 and 2x3 dimensional cases the… …   Wikipedia